Your Jirachi is completely overpowered at level 89 so yeah it can probably take the whole league by itself. In the case that this is in fact a typo then;
Defog is completely useless on Giratina. Replace it with Earth Power (Level 60)/Ancient Power
Azumarill is acceptable ingame though you might want to change Bubblebeam to something like Ice Punch
Feraligator.. please get rid of cut. Replace it with Crunch/Ice Fang
Azelf. I dunno but I'd suggest running a Nasty Plot set with Psychic, Shadow ball and another move
With Uxie I'd probably replace it with a fire type or something to deal with Aaron easily.
However Azumarill is completely underlevelled and all your Pokemon should be at last like mid 50s or something before taking on the Elite 4. If you do get them to that point then here's what happens at the elite 4: Aaron gets killed by fire types, but if you dont' have one fly jirachi will make do. Bertha is easy, you have Feraligator and Azumarill. Flint same thing. Lucian gets a little annoying, but Giratina can handle it and Jirachi can take out Gallade with a little luck and if you run the Azelf set I suggested, then Azelf has this in the bag.
Cynthia gets complicated. Having an Ice-type attack (Ice Fang/Ice Punch on Azu/Fera) will make this alot simpler since it destroys Togekiss, Garchomp and Roserade. The others, just hammer them dead with like Draco Meteor.

GL beating the Elite4, sorry about the big block of text and hope I helped!

Not editing this into my Answer but. ._. If you sold all your TMs I demand you go right back to Veilstone and ask for a refund. Nah, just go buy like. Fire Blast and Thunder and Blizzard and spam your way through. And get heart scales and go to the move-relearner in Pastoria city and relearn some better moves D:

In regards to the fire type you can grab the electric type Electabuzz at level 39-41 on route 222. Then go to the move tutor on route 212, learn Fire Punch though you need some shards. You can also get Ice Punch if you want.